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   "source": [
    "## The quantum pigeonhole paradox\n",
    "\n",
    "Hi! I'm Maria, and I am transforming quantum thought experiments into quantum circuits using Qiskit. In the latest installment of the Quantum Paradoxes content series, I explain how a quantum thought experiment can appear to violate the pigeonhole principle—a fundamental principle in classical mathematics. . In this notebook, I will show you how to count quantum pigeons using Qiskit, to see how the pigeonhole principle may not actually be violated after all. If you haven't already, take a look at my video about the quantum pigeonhole paradox on the [Qiskit YouTube channel](https://www.youtube.com/c/qiskit).\n",
    "\n",
    "The pigeonhole principle is a foundational concept in mathematics which states that, when you place three pigeons into two pigeonholes, at least two will go into the same hole. This may seem obvious, but this principle is very fundamental in mathematics, and many other mathematical results depend on the assumption that the pigeonhole principle must be true. "
   ]
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"
    }
   },
   "cell_type": "markdown",
   "id": "e13497a2",
   "metadata": {},
   "source": [
    "![pigeons.jpg](attachment:pigeons.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a58e027f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "To test the pigeonhole principle with quantum circuits, let's represent each of our three pigeons as a qubit. The 0 state represents the pigeon being in a pigeonhole labeled “0,” and the 1 state represents the pigeon being in a pigeonhole labeled “1.” Each quantum pigeon can be in hole 0, hole 1, or a superposition of both. \n",
    "\n",
    "We are going to start each of our three quantum pigeons in a superposition of both holes, so the qubits are in the |+++> state where |+> = |0> + |1>. "
   ]
  },
  {
   "attachments": {
    "triple_plus.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "84343181",
   "metadata": {},
   "source": [
    "![triple_plus.png](attachment:triple_plus.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4f3457e",
   "metadata": {},
   "source": [
    "If all three quantum pigeons began in hole 0, we need to apply a Hadamard gate to each qubit to prepare the superpositions: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b1399ff7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.797x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit \n",
    "\n",
    "q_pigeons = QuantumCircuit(3)\n",
    "q_pigeons.h([0,1,2])\n",
    "\n",
    "q_pigeons.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9ed6bdd",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Next we measure each of our quantum pigeons, in the y-basis. The basis vectors of the y-basis are |+i> = |0> + i|1> and |-i> = |0> - i|1>."
   ]
  },
  {
   "attachments": {
    "y_basis.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "74f4396e",
   "metadata": {},
   "source": [
    "![y_basis.png](attachment:y_basis.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8960817",
   "metadata": {},
   "source": [
    "One way of performing a measurement in the y-basis is by applying S-dagger, Hadamard, S, and then a z-basis measurement: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2d48cb36",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 658.679x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_pigeons = QuantumCircuit(3)\n",
    "\n",
    "q_pigeons.h([0,1,2])\n",
    "\n",
    "q_pigeons.barrier()\n",
    "\n",
    "q_pigeons.sdg([0,1,2])\n",
    "\n",
    "q_pigeons.h([0,1,2])\n",
    "\n",
    "q_pigeons.s([0,1,2])\n",
    "\n",
    "q_pigeons.measure_all()\n",
    "\n",
    "q_pigeons.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3cd3618",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Now let's simulate this circuit to see the outcome of the y-basis measurements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a9b30da1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Running the circuit \n",
    "\n",
    "from qiskit.providers.aer import QasmSimulator\n",
    "simulator = QasmSimulator()\n",
    "\n",
    "job = simulator.run(q_pigeons, shots=8000)\n",
    "result = job.result()\n",
    "counts = result.get_counts(q_pigeons)\n",
    "\n",
    "from qiskit.visualization import plot_histogram\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "attachments": {
    "triple_i.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "0e681a0e",
   "metadata": {},
   "source": [
    "![triple_i.png](attachment:triple_i.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29c18691",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Next, we are going to post-select on a particular outcome. Post-selection means we choose an outcome of the quantum circuit that we are interested in, and discard the other outcomes. In this case, we are interested in cases where the y-basis measurement gives an outcome of 000. This indicates that the qubits were in the state |+i +i +i>. \n",
    "\n",
    "Now between us preparing our |+++> state and measuring our |+i +i +i> state, we want to check if there was more than one quantum pigeon in each hole. We could check whether the first two quantum pigeons are in the same hole by adding C-NOT gates controlled on qubits 0 and 1, and targeted on an extra auxillary qubit. If qubits 0 and 1 are both in the 0 state or both in the 1 state, then either zero or two NOT gates will be applied to the extra qubit, and it will be a 0. If qubits 0 and 1 are in different states, then one NOT gate will be applied to the extra qubit and it will flip to a 1. So, we can measure the extra qubit to find out if the first two qubits are in the same state or not: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8957bf1d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 387.597x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_pigeons_same = QuantumCircuit(4,1)\n",
    "\n",
    "q_pigeons_same.h([0,1,2])\n",
    "\n",
    "q_pigeons_same.barrier()\n",
    "\n",
    "q_pigeons_same.cx([0,1],[3,3])\n",
    "\n",
    "q_pigeons_same.measure(3,0)\n",
    "\n",
    "q_pigeons_same.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "36505bd2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Running the circuit \n",
    "\n",
    "job = simulator.run(q_pigeons_same, shots=8000)\n",
    "result = job.result()\n",
    "counts = result.get_counts(q_pigeons_same)\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "attachments": {
    "after_cnots.png": {
     "image/png": 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5Z8BsCLxgwQJq1sUsotQQBU3wC+qb8Hfffccmy7hQ0DZv3kw+N0gzkIDvTkPVQMOGDTWDQFw+VcENYZOQruzYsYMcAnhaqWlMoXGhoAVrW127dmVrKsB7rlixIu2Mk9SUa3/99Vea5QSef/55tqaOiktxYppJCpKSkvLkyYMqZcqUYZPgEBcKWtOmTePi4uAe0egJAv+nNewVXhS0zp074xDlypWjn4ZCDVckvChoQKXfWrZsGZtMsG/fPjrtSpUq2ftgE2EKWkJCQpjzLrlT0P76179SLXRT6OLYmgojRoygnRGj6qd4a9SoEargB2VwfnE0o8Yv/PDDD2xygjsFrUuXLlTr7rvvTjNrj5pblClTJk2xtXv37ughK1SoQHqrIkUn7EVBA++//z61g/iQTYJDnCpoX331Ff6yCBxULEDcG4A3AnhR0Fx7gHipaXqAKgO18fRban4xvBc2WSCSFDTQrl07upzVq1ezyTJOFTR0MnjyK1eunOLJL168eIqvp14UNHshMK4UzcL3++WXX9jkDf8qaN9+++2gQYMyeqaJLVu2fPjhhxl9BhPOH1eBa+FtO2zcuJGerrDFG04VtOPHj6u5mXCDdEKvyZMn0/5g9OjRbE0L6tfy5cunP3JNsIfyBlx8fyacKmhJSUkPPvggHbREiRI63aB664COHTuyNXXw9FLeGZA7d26dPmrPnj0qy/IzzzzD1rR44403qMratWvZ5GPQC/Xu3dtXDpkLBa18+fJUBUE+IrSnn356zJgxiPZ/+uknshNeFLSGDRtyKzExd91115/+9KchQ4bs2LEDXRZbA3hU0Oyl31I/anurX4VTQVuxYkX//v3TFIw8QgvDA/yh2WQTFwoarRRBzJs3j62pg8hT9bRFihQ5e/YsF4Tkiy++oCo9e/Zkk485deoU+rQNGzbwts9YvHgx3Uz0IWxyiAsF7ZNPPqEqYOrUqWxNHbwuq1WrRvvnz5//xIkTXJA66scC4MvVqVNn4MCBFFgGf9jwqKDhpUztPPvss2zyMXg74DWxcOFC3vYHThW0KVOm0D0HsbGxqN6lSxe8ptGZUO5OhWsFzYUHuGrVKtofdOrUia1poTJQm02/hd6GziQuLo5NFgibgoYXa79+/WxndlMhcKtWrdhkGacKmvqQAO688048+V27dl26dCme/CeffJILAnhR0IClEFhNlUXnzCZv+FRBg+tJU2Ez+jrNNL7x9ddf5+2MCX3UtdoVEjQiBn/6ixcvsskmThU0NUoOaHamcLzUJ0e8a48ePcoFIUFnTVVc5AQRzLJ9+3bydwsXLux6/rxTBW3YsGGBv//v6M8bffnll6kKTjjNj/nz58+nncH777/P1rT44IMPuE5MzOzZs9kaku+//572b926NZt8DKXm1ZEgw4YLBW39+vXwp3fv3p3C/zCooMFDQh+IBhMTE9kUwKyCBtA/ox10ni5y/IVAufhlypSxtKRA2BS069ev02DnQYMGsckOSuwIT94lpwraqVOnyG8E+lHB6tWrqQrQ7KPwIqAbXrx4cXejksNJ586dcarly5fnbZ/xyCOPBO59jP5E2hQ4VdAQD1POEFC2bFm2psWPP/5IA3aATgAGz2H58uU7d+681Zs1qKCB2rVro50sWbL4fyTOtGnTcKrZsmULj4eviVMF7fjx48uWLcPzcOvQRVMKmjsPsHnz5lRFxwMk0LVSFePptx577DFq2Xv2wNQIm4I2cOBAHAV9vu3enmTTsIXAThW0Y8eOpfbkm1XQLIXA165do3n0+IEYGRLkUwXt8OHDdKB33nmHTRkTWt7O9bc1n0CfKe666y7etoaaUqEfK3rBkYJ25MgRNQCncOHC+j3pxIkTqRZ466232BqSo0ePkq+GO88mIZ1o1qwZ/e169+7NJuc4UtCSkpJoRXCQNWtWzWERYMWKFVQLwJNjaypUqlSJd42J2bp1K1vT4sCBA1wnEJJpzoAjWSpXrlwp1BYfQitePf3007ztA1woaKlhUEFLDeMK2pgxY6gp45/T1IRTSx8qwqag/frrr3Sgv/71r2yyA956NE0JYT+cUbZaw6mCphaZBUOGDGGrBuQJgCxZsmhOzCRZClidpmSEZ599FueZPXt23vYTS5cupdtYsmRJ19GpUwWtb9++tD9wtEoJqfkAAdj27dvZ6hyzCtrUqVOpqaFDh7LJr6h8sqZmURnBqYIWAiMKWgoPUD8f//Lly6kWSNMDJPCSspSB+ssvv6Qz0RdonBI2BU1lBrA9ynv48OF0oMmTJ7PJJk4VtBCYVdAQblsKgeEY0BkaGYYmCppdREFzxOnTp/HCwLFq1qzJJps4UtCCvfM33niDrRrs3r2bqwW+LWguZEb9EToRR0sfCmZBP05JTDJnzqwzcSM1HCloEyZM+P1ZCeCo67h8+bISeeGj79q1iwtuQYkyoFSpUmzVIzgX8q2Ll90WNbVq2rRpbPIroqB5xLiCZi/9lkqNb8nFjzwFDfTo0YOO5XrEkD6OFLSLFy/mzp2b9gd79+7lAg1ef/11rqY9AWr79u20/0svvcQmv+JnBU1NBvcyfNKRgoZfpcpOCxyNRHj77be5mrch1WYVtMTEREpLVKFCBTb5FVHQdAj2AOvWrctWDZKSkuBkUsXQHmAwljJQX7lyhXLgAkvzHyNPQTt16hSFwLVq1WKTTXyroIH69eujHeMhMGI66n4R03lPYyoKml1EQXNK48aNA3/5cLxi9RW0q1ev0p+ScLogo5oyADRHUsyePZv279u3L5uEsNO9e3f6K3h8nzlS0IJHhzldNSYuLo5rhpxp9dxzz/FOzj/FqARSAL9WtoYELw4SIh977DE2+RVR0DxiXEEDTZs2pdZ27tzJJhOcOHFCTcuysXxNRCpoe/fuJQc0DHmXHClowZmt8MJlqx54oXPNmJi8efNqDq+jzjZ79uyaX8XSC98qaLt371Zakhd/z5GC9umnn9LOIFu2bI6GUn7++edcMzCv3HWaZrMKGnjttdeoNd9muyNEQdMh2APs1q0bW/X470CudCLN9QeITZs20f7G02+pNeIbNWrEJqNEnoIGlHOO7pFN1vCzgmYvBFaTD7xnaxEFzS6ioDnlq6++CvzlHb85XKCvoAWnaQerVq3iAj2CdQ3N4BzRF2449jc+uNq3IKBt3LhxvXr1fOJd4bYXKVKE/moDBw5kqyv0FbSjR4/SEQmnoomacwrKlSvH1v/LlStXVLYg0KNHDy7QQ6mKIHfu3Jq54SiKQ+TgaGxI+BEFzSM2FLQlS5ZQa8bTb9WpU4datrHwcUQqaODRRx/FsbJkyXLy5Ek22cGRgkbrYxJVqlRhqx4rV67kmgE0l0IbO3Ys7T9u3Dg2+RLfKmgqqyYCOTa5wpGC9tJLL9HOwKloorQG4ptvvuEChxhX0NasWUOttW3blk2+RBS0NEnhATqdzae+NgH91IeWMlDjB0JnkjVrVrNpTImIVNBUCAxPm03W8LOCZi8EHjVqFJ1k4cKFPbYsCppdREFzSnJyMq13WaRIEUsJnhX6CpqaukI4HfwZrGvkzJnzypUrXBCSN998k6o4FewyKOhz6XrDIJ7qoHKNA/1MYbdFX0ELXuYJOE2yE5zpHxw6dIgLgkgRLk6YMIEL9AheXhZoPpwqGMYZssmXiILmERsKmkq/VbBgQbPpt5QvVaxYMTaZI1IVNEoHDmznXdJX0K5evRq8vv7zzz/PBXocOXKEawbQXFnl3Llz2bNnx/5OBbsw41sFTa026DGg0FfQEC8FT+GsV68eF+hx/vx5rhlAM63trRhX0ECZMmXQWt68edEDs8l/iIKWJik8wKVLl3KBHilCFc0ZcCoDtdn0W+iW1cda1wvZhyAiFTQVAhctWtR2COxnBQ1YCoGVvgQ0F9xIDVHQ7CIKmgtUxrFFixaxyQ76ClrVqlXplAC8H81xN4ouXbpw5QDLly/ngpBs3ryZ9rcdgPkExMn0e6lWrRqb0hXli3iPrvUVtOAv5EAzk4Vi/PjxXDPAbdUxxIdcHMDpr0ytx0doyp3Xrl2j5Lj33nuv64zRYUAUNI/YUNCAkoYXLFjAJhOoPhZs3LiRrYaIVAUtMTExV65cOJztvEv6ClqKQeKaucwU6JG4ZgDN1KhAfRvbsWMHm/yHPxW0/fv3060DeKew1RX6Clrw7x24yGUWPHwbDiRbHWJDQRswYAA1aEOqMIUoaGmSwgP8+eefuUCPcePGcc0AEydO5IKQqAzUxtNvIfilM2natCmbzBGRChpQIbBmomHX+FxBw8+HWjPuQZUsWZJa1vxalhqioNlFFDQX4J0R+OPHNGnShE120FTQrl69mjlzZjol4MITTTEySH9KICVEgNN24cIFNkU0tBq3x7T9plBfyL3HpfoKmurZiaNHj3KBHmp4CHHbCCE+Pp6LA6xZs4YL9EgRrOqrMF27dqUqS5YsYZP/EAXNI5YUtH379lHY+azR9FvXr19X6eeNj46MVAUNoGOhI3r8hBsafQVt0KBBtCfRs2dPLtBGrcECMmXKpPmRTP023377bTb5D38qaCNHjqRbB/cGvxS2ukJfQVMTbwmnSivInz8/Vw7gLgWeDQXt2LFj5KY6yj0fZkRBS5MUHiD+rFygh1qYlWjTpg0XpIXKQG02/Vbv3r2pWbxnNSff6BOpCpoKgV944QU22cHnChqwFAK3bNmSztPjV0BR0OwiCpo7KNXfH/7whzNnzrDJApoKGoI37KbImzcvF2jTv39/rhxAfylPNcnIe/CcIZg5cyZd74ABA9iUThw4cIDOBHz55ZdsdYumgpacnEwZ9xVOn3+VfZO4bc9z3333cXEAp0Nvgie3Av2lPHfu3ElVmjVrxib/IQqaRywpaOCxxx5Dg/iBmHWXlef34IMPsskQEaygKc3Cat4lfQUNp0F7EnjhcoE2eK1z5QCa6RqvX79evHhx7H/PPfeYnV9sEH8qaOh8AnfaQJZxfQUNAQXtSbjIF0HTyRWOlvJU2FDQAMk3mTJlum32Bj8gClpobvUAz549y2V6BC92AfTl1K+//pqqmE2/tXz5cmoWGP90GqkKGqhevToOly1bNqcPgCP8r6BZCoEnTpxIzQIvqZlFQbOLKGjuUGtj6aSGdY2mgrZixQo6GaJQoUJcoI3KMkDUr1+fC9LizJkzfwisTl2zZk02RTR4P9H8IATe6bt+QvBgeO8f5TQVNDi+dERFYmIil+mxcOFCrhmgdOnSXHAThHw0XF+xfft2LtMD+3PNAGhNf1ZmtWrVUAWxnG9XrxMFzSP2FLTp06dTm8OGDWOTCfr06UPNAqcf/EMTwQoaKFu2LI5oNe+SvoLWoEED2pNw8YSoRWOIZcuWcUFa9OzZk6rgbNnkM3yooOG9pl5DTtebvhV9Be3FF1+kPYnevXtzgTb02CvcfV2zpKDNnTuX2kSfxiafIQpaaG71AJ2u95rCA7xfe40OS+m3cP5qwevOnTuz1RARrKCpEHj06NFssoD/FTRLIfCOHTvoPMGYMWPY6hxR0OwiCpo7Lly4QKFspUqV2GQBTQUtxcy4kiVLcoE2wQvtAzhhXKBBkyZNqJavfA57qJei7Sx4oWnTpg2dBl7/3gefaypoakUthVNXBoEf1wyAI6YQIlOs9AT27NnDZXqkGJIJjhw5wmVpoX4IY8eOZZPPEAXNI/YUNPjiNtJvBQ/bdL243m2JbAVNTZz89NNP2WQafQUNjwTtSbjoXkqXLs2VA+hn1N6/fz8JIs888wybfIYPFbT169cHbvPv4KXAVrfoK2iPPPII7UngGeYCbWhWkWLEiBFc4ARLChocFYo4SpUqlb4fIFNDFLTQ3OoB6n+eJJYuXco1A9zqAYbgvffeo1pmfW8apQvi4+PZZIgIVtBUCFy5cmU2WcD/ChqwEQKjq1TCrv5M51sRBc0uoqC55pVXXgk8Ai7HyeugqaAFD1IAjvQvYsaMGVw5AHxZ/bcaXmZUyycrVNpm37591LU9+OCD6TgvRq0dYWSRPk0FDbEoHZTIkiULF2ijYglFikxq69at44Kb6OtfxPHjx7nmTfQzqcH/iI2NRZW4uDg2+QxR0DxiT0EDStfesGEDmzyzceNGahO4iKhDENkKGvoB23mX9BU0klYVLlaUU1kvCUeZ1OrUqYMq6K5PnjzJJj/hQwVtwoQJgdv8O97ndukraClGGrrQvyjBiKJjx45c4ARLChpQmsLKlSvZ5CdEQQtNGDzAEFhKv0XdI8ifPz+bDBHBChpQIbBBNSoFGUJB++abb6hNsyGwmo/vZeU6UdDsIgqaa1atWhV4BNwvGZ4mmgqaCtsIvG65QJt58+Zx5ZvoZ8q/fv160aJFUQXOn8HB1X5GvTnMTtfSB/eclBRQu3ZttnpAU0EbOHAgHZTImTMnF2izZcsWrnyTtWvXclmAFGkywOnTp7lMjxQr+oOZM2dymQYtWrSgWtu2bWOTnxAFzSNWFTSl/xpMv5WQkEBtgubNm7PVBJGtoIGGDRvioJkyZTp48CCbjKKpoJ07d452U7gYFkcTzBUtW7bkAg3UF7IhQ4awyU/4UEHr0KED3THgPUmCpoJ29epVNe6AGD9+PJdpU7duXa4cAPeWC5xgT0HbunUrNevoAQ4boqCFJgweYGhsZKBWy86A48ePs9UEka2gqRDYnt6SIRQ0hL02QmAl7ObIkcP1iF1R0OwiCpoXaGIF7qHxNVwITQVNDSIl0tz/Vr788kuufBNHa1R3796dapmdZORb8JalMQVwIA4cOMDWMAL3jm44eOWVV9jqAU0FTY2iJ/LkycMF2mzbto0r3yTFM5NiQjFISEjgMj0uXrzINW/iKI+AyixrPCmGEURB84hVBQ0gzkGzZtNv5cuXj87W7GICEa+gffHFF3Tcjz76iE1G0VTQgld9IT7//HMu0ybF2CJHUzKTkpJoRdfy5cuzyU/4UEGrVatW4DabSZKgqaCdOXOGdlNMnDiRy7SpX78+Vw6AMIwLnGBPQQNwUNEsXmThjPY1EQUtNGHwAEMDH4NqpTmcU58BAwZQm2Dx4sVsNUFkK2g3btywHQJnCAUN2AiBg4Vd14sJiIJmF1HQvNC3b9/AUxAzd+5cNhlFU0FTyzwTRhQ0hLJcpsHu3bupVpMmTdgU6UyePJkuuUKFCuF3BFVkCD788EO2ekBTQUN3RwcljPhPX331FZcFCF4hgfCuoDlytuAW3BdYDLRAgQJXr15lq28QBc0jthW0wYMHU8ufffYZmzwTFxdHbWbNmtXgzPGIV9Dw+82fPz+Oi7+y66+4IdBU0G7NzOhdQXO6QOTrr79OFX/44Qc2+QYfKmhq5VMjSRI0FbRTp07RbgrvCtqjjz7KBU6wqqCNHj2aWp40aRKbfIMoaKEJgwcYmgsXLuTIkQO1DKbfCs40anaUbmQraECFwPPmzWOTUTKKgmYjBA4Wdt0tCANEQbOLKGheOHLkCI26b9CgAZuMoqmgkQOqMKKgOV0Akb7Zmh1c7XNatmxJ9wo+a5gToikfFEydOpWtHtBU0N5++206KGHEf0IUymUBgi+N8K6gOc0m07t3b6o4f/58NvkGUdA8YltBO3HiBK33bzD9VtOmTelsgcHlOCNeQQOdOnWiQ69YsYJN5tBU0JR7rfCuoDl1OVRq/DfeeINNvsFvClpSUhLdKwDHhq0e0FTQ0HXQbgrvCpq7FeKsKmh4oWfLlg0tV69enU2+QRS00ITBA0wTvK2ooqkM1Js2baIGAd4XbDVBxCtohw8fphAYzxWbjJJRFDRgPAQOFnZdL8cpCppdREHzSL169XDozJkzGwxsFJoKGsJp7KYwoqBt3bqVy/SYMmUKVRw1ahSbIp2rV68ijKGrxi/IqdDjhQ8//JCOC1atWsVWD2gqaCocJYz4TylUKjw/XHAT7wqa03R1hw4dIrfAV0IVIQqaR2wraKBRo0ZoGY8QHiQ2eePdd9+lswVOe+YQRIOCZjXvkqaCtmvXLtpN4V1Bg+PBBdqUK1cOFdFpJyUlsckf+E1BU+49MPLYaCpo8CFpN4V3Bc2dSmVVQQMvvvgiNY6fBpv8gShooQmDB5gmxtNvnT59mhoELVq0YKsJIl5BA1ZD4AykoKlpSaZC4O+//54aBL1792arQ0RBs4soaB5Ric8HDhzIJnNkIAUtMTExZ86cqFipUiU2RQGXLl1SgU2ZMmXC5nW1b9+eDgocZaxLDVHQUkD5mH24ep0oaB4Jg4KGR5oa79OnD5u8oeI6sHz5crZ6JhoUNAD/G4e2kXcpHRW0+vXrc4E2H3/8MdV1sY6BVfymoP344490o4ARD18UtBQsXryYGn/vvffY5A9EQQuNHxQ0YDb9VrDH+OSTT7LVBNGgoKkQ2OxC4UQGUtDwFNH8YlMhMM6QThW8+eabbHWIKGh2EQXNIwhCKM1zmTJl2GSOdJzFuWPHDi7T5tVXX6W6mzdvZlMUkJCQQBEawJMwbdq069evc5k11CdcsH//frZ6IB1ncS5YsIDLAtiYxTly5Egu00at2o6wk03+QBQ0j4RBQbt69WqBAgXQeKlSpYyk3+rXrx+dLZg9ezZbPRMlCtqYMWPo6C70iNBoKmiIxmk3RfhncQI1v9hv/p7fFLQlS5YE7vHv9OjRg60eSMdZnO5modpW0OAjFStWDI0XLlzYVwu4i4IWmjB4gDqYzUB95coVag3ExcWx1QTRoKCpELhs2bJsMkcGUtBAq1atqHEjIXCwM9y0aVO2OkQUNLuIguYdtfC5o1WZddBU0J577jk6AcKFBH6rgoZfL5dps2bNGqr71ltvsSk6SEpKevnll+naQcWKFRcuXMhldqCB0wT6IrZ6QFNB69q1Kx2UyJUrFxdoc6v/lCKP7NixY7ngJk7TCtyqoIWOW27L5cuXKZl0uXLl2OQPREHzSBgUNNC5c2dqf+XKlWzygBo9BMaPH89Wz0SJgpaQkJA9e3Yc3XjeJU0Fbe/evbSbwsUqEykUNKcrCRA0XP2OO+44ePAgm3yA3xS04AQ0Rhbq0VTQVPyi+OSTT7hMmxQKmg9XEiB69OhB7X/99dds8gGioIUmDB6gDioDtan0W3QmoFSpUmwyQTQoaECFwOjo2GSIjKWgrV69mho3EgIHuw1PPPEEWx1iUUHD7xaBaDVXVK5cmQ5UuHBhNjkE/lC3bt28D1fZsmULol9u1Dn0TTJ37ty87ZBHHnnktddeO3fuHJ+NW06ePPnKK69wo87JkycPrgLXwtvOadKkieuMDGrMP24FmwyhqaC98MILdAKEixctAgCufBN3DkSZMmVQ96677kJsxiajnD9/vk2bNnjq+M/mJ7JmzUq3jsAPHGGSpcUc69Spw4eJiTlx4gRbPaCpoKHLooMSuGQu0GbDhg1c+SaLFi3isgATJkzggpscPXqUy/QIzmpBjB07lsuc0K5dO6q+fv16NpkAd+CZZ57hh8Y55Djmy5ePtx2C3w6crYsXL/LZmEAUtFvZvn07tW8kj9KIESOoNeBCDk4NRwrasmXLGjRowI+RQ9RaoojG2eSQ6tWrd+7c2fWCLc2aNaMTMJt3SVNBO3jwIO2mmDJlCpdpAzeAKwd49tlnucAJ6lOZ67wqt+Xs2bOvvvqq6/cyDWG44447eNs5zz33HCJzPhvPzJw5k+4S6NevH1s9oKmg4TbSbgoXo6cfe+wxrhwgPj6eC5wQBgUN8SEdpXHjxmwyQXJy8jvvvIPugp8MhxQtWpSu+uGHH2aTQ+rXr//tt9/y2RjCPwpaGDxATUgpNpV+iwJhcO+997LJBPoKWlJSEhxO110ofqR0ILxq2eSQRo0arVu3js/GISoEbt26NZsMkbEUNEAxu5EQ+NChQ3SqABEfWx1iUUGrUKEC7ZyOeF9MRC0ImI64cAdTMHz4cG4r/fAiG9N7t0iRIrxtCE0F7c033wxcAVOiRAku0EYlQVQ4nTpHdOnShaqvWbOGTUaZNm0atZ9R8P7TuC2PPvooHyAm5vTp02z1gKaCFhzJE06nYKgssIqNGzdyWQAVlCr27NnDZXoEv3iIOXPmcJkT4AdTdSPDEBTPP/88NZuOuJhEFgJR0G4LWkb7BQoU4G0PBA/MdLqwbAgcKWgpxkClC65XTfnss8+oBYN3D2gqaMFrOxIuNH3Ez1w5QJs2bbjACfiLU6yIUI1NJvjkk0/orNIRg8Hb9OnTuVFDyX00FbTr16/jFUx7Ei6y61apUoUrB3jxxRe5wAlhUNAAhWB33nknb5tArTmbjhgJ+IPxj4IWBg9QE/VORFDAJg/Q0H5gNojTV9BunQYUftyNayYoBMa/vG2IDKegqWnO3kPg4En97oYSA4sKGl6TDz30UAlX0Bx+kDt3bjY5pFSpUq+++qr3ISrfffdd9erVuVHn0IiG7Nmz87ZDSpYs2bBhQ++jYA4cOFCvXj1u1Dk0RwPXwtvOqVWrlrt+HOzcuTPwLMS89NJLbDKEpoI2dOhQOgHChceTIvmUi7HZBH5QVD0xMZFNRjl58uTTTz+Np47/bH5CfcUi4B1OnDjRSKLTWwkeg2Yk1b2mgnarvHXhwgUu02PRokVc8yanTp3isgBq7TyF00Utbs3b/cMPP3CZE9REvBUrVrDJBEuXLq1atSo/NM6h2CY2Npa3HYLfzjPPPGNqvW1CFLRb2b17N7XfpEkTNnkgeHmN9BqDNnfu3MqVK/Nj5JDixYvTgXLmzMkmh+DPhNer60UkzSYoUWgqaKBgwYK0JzFkyBAu0EbdQ6Jv375c4AT1VcBsBvejR482aNDA9XsZvRlOCT0bbzunRo0aBnNoBI9B69+/P1s9oKmgAYoYFb169eICbVKMDHCXZyYMCpqaiOcio18I0Ke1bNkS3QU/GQ6h6SygaNGibHLIww8/bHylDv8oaLcKPU7Hs6fpAWpCU7/xoO7bt49NHlDKdXqNQTt37lzjxo1dd6G0jBvAa4JNDomLi3M3GBCoELh58+ZsMkSGU9AqVqyIxo2EwOgh6VSBu6HEQPKg2UXyoHlHDbxCbMwmQ2gqaF988QWdAOFC/xo8eDBXDgAnjAucsHHjRqru7vN4xuXGjRvdu3enawf4e+FVZCSDeGrQA0+gn2WrBzQVNLx16KCKND2DFMybN49rBkDsxAU3USmTFN9//z2X6aGGlCtcSPzGk8GbQvKgeSQ8CprqEFx7pcEMGzaMWgPupiTfFkcKmhfSNw+a8UWyFPoK2iOPPEJ7Ei4Wac2fPz9XDjB9+nQucIJK+OCrNE9+y4OmVpcDRqa76itowW924CK+oKGvitGjR3OBE8KgoJlNBm8KyYMWmls9QKf6V5oeoA4nT56kL9aulYUUkJgLzPoD+gqaR9I3D5oKgZctW8YmQ2QsBU3NUDYSAh84cIBaA3Xr1mWrQ0RBs4soaB65du0aTUEvUaKE8UhbU0FLIRng1cIF2ii/gXCXnlPljXI9nT4jkpiYSPITgN/ZtWtXS7nPggnOfId+lq0e0FTQbpW3nGakDp4gA267fA9+yFwcwGkudrWiBZEtWzYXP0ylSruIda0iCppHwqCgJScn06SGYsWKGVmZN/gLh8EBDlGioOGxpKMbHL5H6CtoKhEb0b17dy7QhgZqKVysUHHmzBkaalGzZk02+QO/KWiLFy8O3OPf+eCDD9jqAX0F7fXXX6c9iQ4dOnCBNuSOKtwtamRbQcMbuXTp0mg8f/78lsbpu0MUtNCcP3+ea97EhgeYJkOGDKHqM2fOZJMH8DRSa6By5cpsNUE0KGgqBC5ZsqTxEDhjKWht27alxo2EwGoeA3A9lUEUNLuIguYRNarZbLIkQlNBS0hIoHNQOBVxUqyw065dOy7QBnEprV1o5DWfUcDLQ300xlvEeAbZ1FBiJfjJ+aqpt6KpoAHK+qxwevTx48dzzQD16tXjgiDwwHNxgG+++YYL9FiyZAnXDIAfERc4oWHDhqibKVMmI0udGkQUNI+EQUHDE0uNv//++2zyRr9+/ahBgLvNVs9EiYJGGdyyZct29uxZNhlCX0ELHqQMOnbsyAV6IDIJFjXA/v37uUwbNRd48uTJbPIHflPQNm3aRDcKdOnSha0e0FfQBgwYQHsSLhanUvO5CKc5EAjbCtrKlSupcac/BNuIgpYmKTxAp2uz6HiAaVK+fHnUzZMnj+t5/cFcuXKFTga4O5/UiAYFzdLqNEQGUtDwKNIccFMhsJobC1yE5IQoaHYRBc0janl4I0OBUqCpoAGVvoFw2o0GKzJg6NChXKDNp59+SnUHDx7MpihAvbfi4+ONrImpSc+ePem4wEhEra+gpZC3nHpgKXL23fbFkCLX/rx587hAj/nz53PNAHhxcoE2x48fz5w5M+qiY2GTbxAFzSNhUNDUA+x0EYzUCF4rxvvqQ4poUNB+/vlnOvQLL7zAJnPoK2gTJ06kPQmn9yExMZFrBkBH7WKkM8XhOXLkMLsUr3f8pqAFr53atGlTtnpAX0HDg0R7Ek5T6964cYPeXESmTJncRdS2FTS1AJo7gc8eoqClSQoP0GlmSR0PMDRqsQhTb5PgtafMZvKKBgVNhcBORyPqkIEUtFmzZlHLpkLg5cuXU4MAER9bHSIKml1EQfPCiRMnaDa+jUgP6CtoDRo0wJ4KpyODUlTftGkTF2iDRwgVcTfCKSSlL2okeeXKlS9dusTWsBCcWXzSpEls9YC+gvbWW2/RcQmnk0RSrBs7e/ZsLggixcq8uFgu0CNFdReLqQ0cOJDqphkYhx9R0DxiW0E7ffo0zZWrXbs2mzzTqFEjOltgJO8hEQ0K2rvvvkuHtjFAWF9B27FjB+1JNGzYkAv0SFHdRfYfleqhVatWbPINflPQgvVKI4uW6itoKRaSdroEW4rqcXFxXOAQqwoaegN6i+l4tmFGFLQ0SeHCffXVV1ygh44HGBo109lphtzU+O6776hBYFY6iHgFTYXAljSEDKSgwVlFswZD4MmTJ9OpAqdBkEIUNLuIguYFlZ5m1qxZbDKKvoI2btw4OhPCqa5BByLwSDjN3XPw4EFyuXwV2Fvln//8JyUfLVCgANxWtoaLuXPnBv5Wv2MkUYu+gqbkEmLEiBFcoEfwaww38LaLQu7Zs4f3COC0M08xoNKFj1imTBlUzJcv32+//cYm3yAKmkdsK2hqvf+pU6eyyTNqfb3MmTMbTBsU8QratWvXChUqhOOaSkiXAn0FDeBJo52B0+w/KZbAGzBgABdo06FDB6q7evVqNvkGvyloIHfu3HS7ChcuzCYP6CtogBY0J4oUKcJWPYKHLQAX6fYIqwrahAkTqOUxY8awyTeIgpYmKbJk2PAAQ3Dp0iX6bbpb7uy2TJs2jc4HDBw4kK0miHgFTYXAxtefJTKKgnbgwAHjITAiOzpVMGfOHLY6RBQ0u4iC5gW80nDcvHnzIipjk1H0FbTghW/B8OHDuUCD5OTkrFmzcs2YmBdffJELtPnwww+pLhx9NkU0SUlJFA7hvn333XdsDSO7du2iGw5eeeUVtnpAX0FDAK+iC+A01TG9EYkQ70X6ZRHw+diqB/UGRP78+Z0mN1ULEbjI4hwGREHziG0FjQJgI8uZK2gpSeAu73JqRLyCtnDhQjpujx492GQURwqaiqYAelpHip4a70xs3LiRC/TAH5qyF8GjYJOf8KGCRrnzAOIi75q1IwUNzyrtDHB0R8PblThFrFixggscYlVBq1atGprFnzshIYFNvkEUtDTBzwFvN65vzQNMDbUQgYtUM6nRu3dvahO4W3kjNSJeQbMdAmcUBU31GwZD4BYtWlCbYOfOnWx1iChodhEFzTXKK2rbti2bTKOvoIHKlSvT+QBHMzW2bdvG1QI4VbsRCZQoUQIVCxYseO3aNbZGNMrH1XGIbZCcnAwHlM7hscceY6sH9BU0ELwSqKOpahcvXqSBe0SIz31q7hUoVqwYW/WAx881XUXsr776KtV14VyGAVHQPGJVQdu4cSM127p1azZ55tSpU9QmMJvMK+IVNOrW7rjjjr1797LJKI4UtGXLltHOhCOfONiZxhPrdDwdTo/quhi8FgZ8qKC98cYbdMeA94fHkYL2ww8/0M6Eo6lq7du352oxMYUKFXK9LLg9BU2lx27WrBmb/IQoaDo0adKE61vzAFMD7i4qZs2a1aAmhdcfnQ8wm8wrshU01a25znOfJhlCQcPruHjx4mjTbAhcq1YtOtVs2bIh4mOrQ0RBs4soaK5BjBR4BGI2bNjAJtM4UtA++eQTOh+AfoetGgRPty5atKjTLkDFz0ZWrfI/p0+fjo2NxfWWKlXKdb/mHTwVdNtLlizJJg84UtCCQ0GEPfqf6FetWsXVAhVxJ7ngFnbv3h2cEVnfrUmRCGbbtm1coAc8PBrvA5+VTT5DFDSPWFXQ1HLmcC7Z5JngiLpv375sNUFkK2jwBmlstZFvDLfFkYIGP7ts2bK0P5gwYQIXaBBc0cXgC3KQ0KMeO3aMTX7Chwra2LFjAzf7d5YvX85WtzhS0EDw11BHf+4qVapwNW+rw9tT0OAlUrN4a7DJT4iCpsPSpUu5vjUP8Lbs3buXnkz4q2wywaOPPkqnlDdvXjYZIrIVtNdee40O6nRMtD4ZQkGzFAIjGKdmNRWA2yIKml1EQXNHYmIijWSuWLEimyzgSEHDa4yEcAKxKBekRb169biOq8wUzZo1o7o7duxgU0Tz0Ucf0fWOHz+eTemB+m6WJUsWp0MSbsWRggZq1qxJRwf6496Dv5B37tyZrakQPOxCP49m8HQnF27W3//+d6o7cuRINvkMUdA8Yk9BU8uZm51rOXv2bDpVsGDBAraaILIVNLXo27Rp09hkGkcKGpgxYwbtD/QXE4CvrxSNe+65x+lKmocOHaJxHw0aNGCTz/ChgrZ69erA/f6dKVOmsNUtThW04LR3+osJBH92Qkd09uxZLnCOJQXt2rVrNEIcnqp3p8UGoqBpoqY5A/3FBIJz1KbpAd6Kmvxhdq6lipsMLv5DRLCChhA4Z86cOOKDDz7IJgtkCAVNhcCu51reCsJ5NVrTy+I/oqDZRRQ0d0ydOjXw948ZNmwYmyzgSEEDn376KZ0VgFfK1pAo3w4gmHQ67D8hIQGOL+pWrVqVTRENwm9yAQsVKoT4k63pQfCKk95HnjtV0NavX6+c7IceekjHG0afifapSq5cudL8/IiLorF+oGDBgjpxI17qBQoUoCp4/biQdMkvxHk6TXAbNiJbQUsxo9zG6CE8SNx6AHjPXOAZtZy5i+VfQ4DWqFlgdtGSyFbQaPkFdDX2Fkp2qqChn0QwQFXA2rVruSAk1DkTTvN2A/XJZ+7cuWzyGT5U0M6fP69ecD179mSrW5wqaECNiwGay8i2bNmSK8TE9OnTh63OwVPKrQRAjMAFnlHKoPdbaomIV9Dq169PF0i4nkAT7AHi9HQ8QLy8HHmAKcAhihUrhrrwvQ1O/kDIo3Tnt956i62GiGAFbcqUKXRER0m3nWJQQatbty6dMGEqSYsKgatVq8YmE+zevZvOE3j5nC8Kml1EQXNH7dq1ccSsWbOeOnWKTRZwqqCBxwNL6hJr1qxha+qobiU2NtbFKl1jxoyh6p988gmbIpovvviCrtdskOyC7du305mAGTNmsNUtThU00KZNGzo60BnloSa4wfH67LPP2BqS/v37UxWgMydFLQwEXGT8+fnnn6lukyZN2OQ/IltBU24ZkSdPHuMTpVeuXMmtB8DTaMq7pb7X4HLmhAqMy5UrxyZDRLCC9v3339MR0U2xyQJOFTSAE6Pl/0H16tXZmjqbN2+mnUG9evWcfuK6cePGfYFFb/Lnz68/2SrM+FBBA1WrVg3cdQM6vgsFbdu2bdmyZaNaOt+ofvnlFyUE1KpVKykpiQucs2HDBmpHYSo5FF5baA1d7v79+9nkMyJbQUNvoD4xEl78dqceoMotqO8BBvPtt99SdbNBd/BHu2+++YathohgBY2ydCEEdqqEOsKUgob+86677grcIWbixIlc5g1LIXDwMGQEJmx1jihodhEFzQVKHn7uuefYZAcXCtr58+cfeeQROr3KlSufO3eOC24HOhHaEz69/kjsYHBuqB4bGxu2jjt9oZn/mTJlsvra0KRUqVKBv14MYmw2ucWFgoZYrnHjxnQCxYoVQ5fIBbcD3o/6/OhoprByQXLkyBE6qdmmTZtovTngLh+BWr5g0aJFbPIfEamgodfavHnz8OHDg5d5JRC+Ll269MCBAx5TtF68eBHPz+TJkwsVKsRN3wQB6j/+8Q/06l4kBrWceaNGjdhkAsQ8NOgVdOvWja2GiGAFTUUU69atY5MFXCho4IsvvqAEbSB0KoCEhASl4+C17mJ11+XLl1P1jh07ssl/+FNBU99v8ObyuK6uCwUNLF68WI3CHjx4MFtvx4ULFyjDOnj44YfRnXKBEy5durR9+/bp06fTSJ9gypUrh4f2l19+8TLu/sSJE6Qdx8fHs8l/RKSChlfnvn378DgFD2wk8uTJM2LEiH//+98uHPjweIAKtYDVrl272GSCjz/+mJqFh2l8WkmkKmgqBMYDwCY7eFTQ1JOvsvIr8ubNO3LkSHdPfjCWQmAlN5cpU4ZNrhAFzS6ioLmge/fugT++g/n/7nChoAHEijREDuClu2fPHi74v6glnBH4zZw5k61OQO9DLbRo0YJNkU7hwoVxvUYGFXunc+fOdP9xVmxyiwsFDeD9pFIAFCpUaP369Vzwf5k6daoadoGnjq3aoI+lujlz5kwt/8WSJUsoKQN49dVX2eoEXAtpK/AFdaYkpBeRoaCNHTsWvjvIlSuXihJDkzlzZvi4uXPnpoppDsb5+uuvaU8cgm5ammTKlAmHwP5UMbWe87ao0Gv+/PlsMoFa3BMYF4MiVUFLSkoiKdb4qL0UuFPQADwHNcII7sSNGze4IIhDhw7h/GmfChUquEtr9fLLL1MLW7duZZP/8KeCtmPHDrp1wOPgFHcKGli+fLnquxDU3HZA7okTJ9TKAwg4T548yQVpsWLFCuro9HtI+IrBPWTob1opUCPE3Xmb4SFiFDREQ/gDoRvE30sNTgwNXsTqL6uZnSaFB5jaurHBHuBHH33EViecOXOGBDidcbuOqFOnDp2YjfEQkaqgdevWjQ4HL4tNdnChoNED7PrJd5QnwV4IrHLzde3alU2uEAXNLqKgOQVOTJEiRXC4woUL216K0Z2CBi5dutS2bVv60I3b0rNnT5UTKjExER6Mmuz54IMPLl68mIqcol4PcMXYFNEol/rdd99lU7oSPB9t+/btbHWFOwUN4CeAp4vUK4RAnTt3Vl7U1atXEWE+//zzgRP8PeGUa9d59OjR+fPnRyOZMmVq3br1smXL6Kd3/fp1/L9Vq1b0qKM3GzlypLtf5cKFCwOnGfP++++zyZdEhoIGB52qgGzZsuXNmxfdVGjwjAX7Q2mOF5s/fz7vGphrAN+IG0odeFHK0Qf6g+fxHJLHU6BAAafz7ELTp08fOpmCBQsaF3YjVUFTCfs//vhjNtnBtYIGVq1ahZcvVY+Pj581a9aFCxeo6KeffurevTuNPcQD2b59e3dDns+fP0/ytE8++aSGPxU0ULp06d//PDExnTp1YpMrXCtoYP369fjzUfUaNWpMmzZNDTHbvXt3r169yB1F34g3o6P540uWLKFmgWYPibg0uIfcvHkzt6UBrSeLo3iZYWqbiFHQVBpyPBh4dfLfL3XwClaaPujfvz83lBb6HmCJEiXQy1GRU0aNGkWNTJo0iU0mQJerhgNPnTqVreaISAUNf3Hqc/CvO2dbHxcKWuA2/I67J3/gwIHckAaWQuDgjzcucisFIwqaXURBc8rXX38d+MuHQ0ZxraARBw4ceO2119TYafytCxcurDoLeIeTJ092HZUhgqWH57777rvtJ/TI49ChQ3BhH3roIY9ylSnw9sIzT39NjytauFbQiFOnTnXt2pW8KAAvGS9X9Vm7UKFCCGU9jpC/ePEivDrS0QCOVbRo0VyB9XAB3oLdunVzN3uFoDsAHI08Cj+RoaDhr4lnBv867X/Q7Zw7d+748eO8nTqI0+APwEV26uTB74cbilj0mva8UXUHXKwvFho1JR89OZvMEakKGs1oQ6hvNiHdrXhR0ADem7Nnz6YVDwC6X3Sb9FalTQSfXiL5cePGUVPupk2FDd8qaGqUd/ny5dnkCi8KGoEnTQ00Q8wPR069CrHZqFEjFz7J5cuXT548iR5Sv6MjsD/1kPpfC9auXUtnG54ewDURo6DhFYkXpdO8BHgdJyYm4tWs1HxNbusBqtHl3j1AeN1oJ0eOHE5PLDQqr7GlxCwRqaCpEPi9995jkzVcKGjHjh0Lz5OP55nir1KlSpkNgdXMYnTyHjVKUdDsIgqaU9TMfy/p/TTxqKAR+J2vX79+xIgRb7/9dseOHXv06DFv3jz0Mlzsljlz5tB9cDcqWzBC69at6a9Qv359NrnCo4JGoK/fsmXL+PHju3TpgietW7dus2bN2rdvHxebAC+qn376acqUKeh4cQj8+/e//33nzp0eX2B4cdCnSOPLmRsnMhS0CEPNZHGx/GsIzpw5o4YSrFq1iq3miEgFbe/evZSQLgy/EY8KmgKv4/nz53/wwQfo0/CaHjZs2Lp167wEnERcXBzOLXv27AkJCWzyJb5V0PBXCPx5f+fIkSNsdY53BY04efIkHrlevXp16tQJzwkCrTVr1vh5SJeCEsiC1Cb6+YSIUdDSBUse4KZNm+iPYvw9pRZDaNiwIZuMEpEKmgqBw/Ab8ZgHzSqzZ8+m++Bl4ePbEh8fTy17F7JEQbOLKGiOOHXqFEXaNWrUYJNNjCholnjyySdxbgjwDh06xCYh7KgVObNkyaIzMCc1jChoGZehQ4fSbbQxkt8soqD5DbWceZUqVdhkCLUyKSIoNhklIhW0Hj160LG+/PJLNlnDlIJmA7XGXLNmzdjkV3yroIFq1arRbXQ0uycFphS0DEpiYiKNTqpQoQKb/IooaD6kffv29Ef57rvv2GQClfoWLF26lK1GiTwFTYXANWvWZJNN/Kyg1a9fH+eGEPhwyDU0nHL69Gm6w2h57969bHWLKGh2EQXNEcOHDw/82cMUK/pWQTty5AgNjsCdZ5OQTlA/Dvr168cm50S5gkYTqXLlyuVxzbUwIAqa31DLmYdeV9EFNIYITJkyhU1GiTwF7fr167SSYMGCBZ3OTXOBnxW0Tp060bnh58kmv+JnBU2NtS9durTrkc5RrqCpLwFDhw5lk18RBc1vXL58mdZYv//++9lkCDWGyJ6wG3kKmgqBJ0+ezCab+FZBUyFwvXr12GSIAQMGBG6wGSffpwrapUuX6LPzyJEj2ZQxoenlth1o27Rq1QpXgWvhbWtUrFgRB8qRI8fFixfZZBPfKmj9+vXDiQEfRg7RxqpVq+hvUbJkSddZ7aJZQfv+++/pBrZu3ZpNPob6hHbt2vG2D4hyBQ39M649NjbWSxq+W1GPJX7XZlcnUIRNQUtOTs6bNy8OZHvK/7fffktX1KVLFzbZxLcKGh4YypNVokQJ1y+FsEFjTEqXLs3bfgKPLqXAB661yChX0GrVqoVrz5o1q20dwTsTJkzAqWbJksVsZ+6RaFbQPvvss99/Od6+EN+W2rVrU8s4BJtMEzYFDS9WHCVfvnwe02alCYXAOXPmDE8I7FsFrW/fvr//XU2/+vHnU6tw/vDDD2z1gE8VNDBz5sxOnTqdO3eOtzMmCL/btm27e/du3s6Y7NmzB1excuVK3rbDhg0b6Olq1aoVmyzjTwXtxo0btEYV+mvvuVoE79SrVy/wYMYsWrSITQ6JZgVNfb5DnMMmH4Morl27dgcOHOBtHxDNCppazvzll19mkyFatGhBLdu7q2FT0MC8efPeeust24HECy+8QFe0c+dONtnEtwoa7jadWK9evdjkYw4ePIg+bcmSJbztM9RYleeff55NDolmBQ3BBV07fAw2+ZgLFy506dIlPONr9IlmBa1u3bq49kyZMh09epRNJti6dWvgqfx9kRB73xjCpqChfbxe0e3zth1UCPzqq6+yyTL+VNDshcBqBfmnnnqKTd7wr4ImRBtt27alp8vsbPwQ+FNBU4Oe2rdvzyYhXdm0aRMlz65SpYq7mSZRq6BdunQpd+7cuPayZcuySXBINCtoykVetmwZm0ywf/9+/BjRLBw1e7MRw6mghYEzZ87QTatatSqbLONbBQ3+N84KLwU8SGwS3IJXKq2Difu5ZcsWtjohmhW0bt260bUvWLCATYJDolZBO3jwIM2Ve/LJJ9lkiObNmweeypg5c+awyQJhU9DCgwqBV69ezSbL+FNBW7lyJd2HDh06sMkQtPY6XjQbN25kkzdEQRN8QVJSUp48efBoPfDAA2yyjz8VtJYtWwZ+ZDGbNm1ik5DeqEWFZs+ezSYnRK2CNn36dLpvgwYNYpPgkKhV0H67uZx5yZIlXedIui00lgrBg40lOBURpqCNGjWKLueTTz5hk2X8qaAdO3Ysc+bMOKv4+Hg2Cd5Yu3Yt3VJ3WW+iVkFLTk4uUqQILrxQoUJhyEsYqUStgta7d+/A78awzvXDDz+EZ73mSFLQ0iUE9qeCpkLgH3/8kU0mgBdBzXbs2JFNnhEFTfAFs2bNokerf//+bLKPDxW0X3/9lXKZ46XOJsEHJCYm0tNSunRpF1mTolZBe+yxx3DhWbJkOXHiBJsEh0Stgqamd8HRZ5MJ1qxZQ8127dqVTXaIMAWN4szY2Fjb2ZQV/lTQVCrimTNnsknwzAcffEB31cWyfVGroH399dd04Rl9ybX0JToVtBs3bpQsWRIXfvfdd1+5coWtJqhRowaaveeee2wLW5GkoOFtQteC9wub7ONDBU2FwJUqVWKTCS5fvkwZ0CpUqID/s9UzoqAJvuDxxx/Hc5U5c2azs/FD40MFjTKtgoy+hkbksXHjRloF2cWKV9GpoO3du5c+RTZq1IhNgnOiVkFTy5kfOnSITZ5B2FClShU0+9BDD5kNG24lkhS0H3/8ka6lRYsWbLKPPxU0chvy5MmTlJTEJsEz165doyk2Dz/8sNNvVFGroDVu3JgufNeuXWwSnBOdCtqyZcvo4TEbzn/++efU7MKFC9lkjUhS0OLj43EhCIGPHTvGJvv4UEFTIfCoUaPYZIL+/fujTYRg7hIFpIYoaEL6c+DAAYq0GzRowKaw4EMFrVq1ajgl/M7PnDnDJsE30OiDbNmyOe2Fo1NB69GjB64azJ8/n02Cc6JTQVPLmdetW5dNJiBHCj/hrVu3sskakaSgdejQga5lxYoVbLKPDxW01atX0ym98cYbbBIMsW/fvly5cuHeOl3pNToVtFOnTtEnverVq7NJcEV0KmgqVdm///1vNnnm2LFjBQoUQJtt2rRhk00iRkHbv38/hcCmMtxr4kMFzUYIjHgNLh+aHThwIJsMIQqakP706tWLnqu5c+eyKSz4TUHbuXMn3YcmTZqwSfAT169fr1OnDv5AZcqUSUxMZKsGUaig4V4VK1YMVw2PysW8V0ERnQqaWs7c4Fr4q1evpnRLI0aMYJNNIkZBw4Xky5cPF3LfffeZTUgXGh8qaK1ataJTMrIWvpACypuJYPLbb79lkwbRqaANHz6crnrSpElsElwRhQrauXPnsmfPjquuXLkymzyTnJz86KOP0p28ePEiW20SMQpaz5496UJsL/eZAr8paDZC4AsXLlCkHx8fb3xZWFHQhHQGzzTNTzY+Gz9N/KagdenSJfDzivnmm2/YJPiMhIQE8rccRcVRqKAhBAo8yzGdO3dmk+CKKFTQbtxczjxv3rymklacPn26aNGiaPPdd99lk2UiRkFTKXg/+ugjNoUFvyloCAtz5MiB86lQoQKbBNNQdvMCBQocP36cTWkRnQpaxYoVccl33nknQkQ2Ca6IQgVt3LhxgV9MzOjRo9nkGZpzUKJEicOHD7PJMpGhoKkQOH/+/GEOgf2moKkQeNGiRWzyTLNmzegabeRvFQVNSGdUfBj+h8pXCtq1a9fuuecenA/CvOTkZLYK/uPUqVNwtvCX0l9fMgoVNFruEOzYsYNNgiuiUEFTy5m3a9eOTd747bffKNWmqQZ1iBgF7YknnsBVmE1Ip4PfFDT8AOl8XKTCFPR55513cJP1Y54oVNA2bNhAl/zKK6+wSXBLFCpocXFxuORs2bIlJCSwyRvz58/HC6JQoUJ79uxhk30iQ0FbsmQJXYXBNSI18ZWCpkLgYsWKmRosNmzYMDRYoUIFS2mRREET0hkVaYchMU0KfKWgzZs3j+5D9+7d2ST4lWPHjpUqVQp/rHHjxrEpJNGmoOFNgYvFJVepUoVNgluiUEFTKVo2btzIJg/AM6MfYMuWLcM5CTEyFLT9+/dTQronnniCTeHCbwoapWjJmjVrhg7YMgSUd6927do6yzVEoYL2+uuv0yWvWrWKTYJbok1B27JlCz08TZs2ZZM34KLA37v77rvD/Lk0MhS0Jk2a0FWEPwT2lYKmQuD333+fTd6YPHnyHXfcUbp0af3hzE5xpqDBI4yNjcUVhnO9VSGyqVChAp6ouLg43g4j8M9w6IYNG/J2utKnTx+cDGKV3bt3s0nwMSdPnoyPj0cHPXv2bDalTtu2bfHHLVGiBG9HOuvWrcP1ggkTJrBJcMu2bdvoZkbP5O5KlSrhehHY8LY3mjdvjn61b9++4ZTPAA5311134UK6devGpgzIokWLAk9fjE5HZ5bvv/+eDu0TmYDy3Ddu3Ji3BZt8/PHHWbJkefLJJ3k7dfbt20fPyZw5c9gU6dSsWRPX+8ADD4S5T4tIaNHnOnXq8Hak8+mnnwZ+LjFLly5lkwfWrl175513Vq5cef/+/WwKF7S0V2xs7G+//camDEj58uVxFenysblWrVo4tN9CYCPDGOGuoKl69epZXZTPmYIGxo8f36JFC3uSnhBtoP9t1qzZ9u3beTuMrFy5skmTJuvXr+ftdOX8+fOtW7eWpLAZiOTk5P79++t47T///HPTpk2jx78Hffv27dSpk8xHNsJ7773Xvn37DO0mOgJ9Ml4KptYdf+edd/75z3/yRniZNm3aSy+9dODAAd7OgFy/fv3999/v3r17+GN1HPrtt9/u2LHjtWvX2JSuLFiwoHnz5kePHuVtwTLfffcd+j3eCEmvXr3++te/OlreJ0OzefNm9JCynIUR/vWvfyEQiJ7RfFevXu3cuXO/fv142xv4kb777rum0pU64vjx4y1atNCcCOJb0jEEXrFihd9CYFMzLWbPnj1o0CBTs0FTw7GCJgiCIAiCIAiCIAiCIAhRhShogiAIgiAIgiAIgiAIghAKUdAEQRAEQRAEQRAEQRAEIRSioAmCIAiCIAiCIAiCIAhCKERBEwRBEARBEARBEARBEIRQiIImCIIgCIIgCIIgCIIgCKEQBU0QBEEQBEEQBEEQBEEQQiEKmiAIgiAIgiAIgiAIgiCEQhQ0QRAEQRAEQRAEQRAEQQiFKGiCIAiCIAiCIAiCIAiCEApR0ARBEARBEARBEARBEAQhFKKgCYIgCIIgCIIgCIIgCEIoREETBEEQBEEQBEEQBEEQhFCIgiYIgiAIgiAIgiAIgiAIoRAFTRAEQRAEQRAEQRAEQRBCIQqaIAiCIAiCIAiCIAiCIIRCFDRBEARBEARBEARBEARBCIUoaIIgCIIgCIIgCIIgCIKQOv/7v/8f0GpvLM5W8YkAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "7143557e",
   "metadata": {},
   "source": [
    "![after_cnots.png](attachment:after_cnots.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "562d1e4a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Our C-NOTs turned the |+++>|0> state into the state (|00> + |11>)|+>|0> + (|01> + |10>)|+>|1>. We can see from this that if we get the measurement outcome 0 on our extra qubit, then the three quantum pigeons are projected onto the state (|00> + |11>)|+>. Now let's calculate the overlap of this state with our |+i +i +i> outcome:  "
   ]
  },
  {
   "attachments": {
    "zero_amplitude.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "c31b5a4c",
   "metadata": {},
   "source": [
    "![zero_amplitude.png](attachment:zero_amplitude.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c0226f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The inner product of the two states is 0, meaning that there is no overlap between the state where the first two qubits are projected into the state, and the outcome where our y-measurements give 000. So given that we got a 000 outcome, we know that the first two pigeons were not in the same hole before our measurement. \n",
    "\n",
    "Now we could follow a similar process to check if the 2nd and 3rd quantum pigeons were in the same hole, and if the 1st and 3rd pigeons were in the same hole. We can see that by symmetry, we will also find that there is again no overlap between the |+i +i +i> state and the states where the pairs of qubits end up in the same state. So somehow, when we get the outcome |+i +i +i>, we know that before we made our measurement, no pair of qubits was in the same state. \n",
    "\n",
    "This means that we've managed to fit our three quantum pigeons into two pigeonholes, with no two pigeons being in the same hole. We have violated the pigeonhole principle!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d18cea54",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Does this mean we need to rethink the fundamentals of how to count when we use quantum mechanics? Not necessarily. The pigeonhole paradox only emerges when we consider the outcomes of measurements that could have been made, but were not. If we actually make the measurement to check if each pair of qubits is in the same state, then perform y-measurements on the other three qubits, they never end up in the |+i +i +i> state if a pair of qubits is in the same state:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9eb878fe",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 808.997x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_pigeons_combined = QuantumCircuit(4,4)\n",
    "\n",
    "q_pigeons_combined.h([0,1,2])\n",
    "\n",
    "q_pigeons_combined.barrier()\n",
    "\n",
    "q_pigeons_combined.cx([0,1],[3,3])\n",
    "\n",
    "q_pigeons_combined.measure(3,0)\n",
    "\n",
    "q_pigeons_combined.barrier()\n",
    "\n",
    "q_pigeons_combined.sdg([0,1,2])\n",
    "\n",
    "q_pigeons_combined.h([0,1,2])\n",
    "\n",
    "q_pigeons_combined.s([0,1,2])\n",
    "\n",
    "q_pigeons_combined.measure([0,1,2],[1,2,3])\n",
    "\n",
    "q_pigeons_combined.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "11f959f5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Running the circuit \n",
    "\n",
    "job = simulator.run(q_pigeons_combined, shots=8000)\n",
    "result = job.result()\n",
    "counts = result.get_counts(q_pigeons_combined)\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0531bb47",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "There is no 0000 state on the histogram, showing that there is no case where the first pair of qubits is the same and the outcome is |+i +i +i>. Critics of the pigeonhole paradox say that the measurement we would make to check if two qubits are in the same state itself changes the state, so we can't draw conclusions about the qubits if we never actually made the measurement. \n",
    "\n",
    "Another issue with the proposed paradox is that we can also check if there are multiple pigeons in the same hole by asking our quantum circuit a different question. Instead of asking whether each pair of pigeons is in the same hole, we could ask whether all three pigeons are in the same hole. Let's have a go: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "71b57a59",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1230.4x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_pigeons_triple = QuantumCircuit(6,4)\n",
    "\n",
    "q_pigeons_triple.h([0,1,2])\n",
    "\n",
    "q_pigeons_triple.barrier()\n",
    "\n",
    "q_pigeons_triple.cx([0,1],[3,3]) # Check if qubits 0 and 1 are the same\n",
    "\n",
    "q_pigeons_triple.barrier()\n",
    "\n",
    "q_pigeons_triple.cx([1,2],[4,4]) # Check if qubits 1 and 2 are the same\n",
    "\n",
    "q_pigeons_triple.barrier()\n",
    "\n",
    "q_pigeons_triple.x([3,4]) #Check if both pairs of qubits are the same, meaning all three are the same\n",
    "\n",
    "q_pigeons_triple.ccx(3,4,5)\n",
    "q_pigeons_triple.x(5)\n",
    "\n",
    "q_pigeons_triple.measure(5,0)\n",
    "\n",
    "q_pigeons_triple.barrier()\n",
    "\n",
    "q_pigeons_triple.sdg([0,1,2])\n",
    "\n",
    "q_pigeons_triple.h([0,1,2])\n",
    "\n",
    "q_pigeons_triple.s([0,1,2])\n",
    "\n",
    "q_pigeons_triple.measure([0,1,2],[1, 2, 3])\n",
    "\n",
    "q_pigeons_triple.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e8dcb2a2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Running the circuit \n",
    "\n",
    "job = simulator.run(q_pigeons_triple, shots=8000)\n",
    "result = job.result()\n",
    "counts = result.get_counts(q_pigeons_triple)\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c76b5ebe",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Now the outcome 0000 has some chance of occurring, meaning that the outcome |+i +i +i> is compatible with all three quantum pigeons being in the same hole. \n",
    "\n",
    "You'll find a similar result if you count in yet another way, and just check the state of each qubit with a C-NOT gate between each one and an extra qubit, then measure the extra qubits. It is only when we check each pair of pigeons individually that we find they cannot have been in the same state. Unlike classical pigeons, quantum pigeons rearrange themselves depending on how you count them. \n",
    "\n",
    "The pigeonhole paradox combines entanglement, measurement and debatable reasoning about post-selection to challenge our basic rules of counting. You can play around with this thought experiment by adding more quantum pigeons or changing the ways you count them. Can you create your own new counterintuitive pigeonhole paradox, or make a circuit to support the idea that there are no problems with quantum counting after all?"
   ]
  }
 ],
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